example

Bob drove his car [latex]525[/latex] miles in [latex]9[/latex] hours. Write this rate as a fraction. Solution

	[latex]\text{525 miles in 9 hours}[/latex]
Write as a fraction, with [latex]525[/latex] miles in the numerator and [latex]9[/latex] hours in the denominator.	[latex]\frac{\text{525 miles}}{\text{9 hours}}[/latex]
	[latex]\frac{\text{175 miles}}{\text{3 hours}}[/latex]

So [latex]525[/latex] miles in [latex]9[/latex] hours is equivalent to [latex]\frac{\text{175 miles}}{\text{3 hours}}[/latex].

example

Anita was paid [latex]\text{\$384}[/latex] last week for working [latex]\text{32 hours}[/latex]. What is Anita’s hourly pay rate?

Answer: Solution

Start with a rate of dollars to hours. Then divide.	[latex]\text{\$384}[/latex] last week for [latex]32[/latex] hours.
Write as a rate.	[latex]\frac{$384}{\text{32 hours}}[/latex]
Divide the numerator by the denominator.	[latex]\frac{$12}{\text{1 hour}}[/latex]
Rewrite as a rate.	[latex]$12/\text{hour}[/latex]

Anita’s hourly pay rate is [latex]\text{\$12}[/latex] per hour.

example

Sven drives his car [latex]455[/latex] miles, using [latex]14[/latex] gallons of gasoline. How many miles per gallon does his car get?

Answer: Solution Start with a rate of miles to gallons. Then divide.

	[latex]\text{455 miles to 14 gallons of gas}[/latex]
Write as a rate.	[latex]\frac{\text{455 miles}}{\text{14 gallons}}[/latex]
Divide 455 by 14 to get the unit rate.	[latex]\frac{\text{32.5 miles}}{\text{1 gallon}}[/latex]

Sven’s car gets [latex]32.5[/latex] miles/gallon, or [latex]32.5[/latex] mpg.

example

The grocery store charges [latex]\text{\$3.99}[/latex] for a case of [latex]24[/latex] bottles of water. What is the unit price? Solution What are we asked to find? We are asked to find the unit price, which is the price per bottle.

Write as a rate.	[latex]\frac{$3.99}{\text{24 bottles}}[/latex]
Divide to find the unit price.	[latex]\frac{$0.16625}{\text{1 bottle}}[/latex]
Round the result to the nearest penny.	[latex]\frac{$0.17}{\text{1 bottle}}[/latex]

The unit price is approximately [latex]\text{\$0.17}[/latex] per bottle. Each bottle costs about [latex]\text{\$0.17}[/latex].

example

Paul is shopping for laundry detergent. At the grocery store, the liquid detergent is priced at [latex]\text{\$14.99}[/latex] for [latex]64[/latex] loads of laundry and the same brand of powder detergent is priced at [latex]\text{\$15.99}[/latex] for [latex]80[/latex] loads. Which is the better buy, the liquid or the powder detergent?

Answer: Solution To compare the prices, we first find the unit price for each type of detergent.

	Liquid	Powder
Write as a rate.	[latex]\frac{\text{\$14.99}}{\text{64 loads}}[/latex]	[latex]\frac{\text{\$15.99}}{\text{80 loads}}[/latex]
Find the unit price.	[latex]\frac{\text{\$0.234\ldots }}{\text{1 load}}[/latex]	[latex]\frac{\text{\$0.199\ldots }}{\text{1 load}}[/latex]
Round to the nearest cent.	[latex]\begin{array}{c}\text{\$0.23/load}\hfill \\ \text{(23 cents per load.)}\hfill \end{array}[/latex]	[latex]\begin{array}{c}\text{\$0.20/load}\hfill \\ \text{(20 cents per load)}\hfill \end{array}[/latex]

Example

Find each unit price and then determine the better buy. Round to the nearest cent if necessary. Brand A Storage Bags, [latex]\text{\$4.59}[/latex] for [latex]40[/latex] count, or Brand B Storage Bags, [latex]\text{\$3.99}[/latex] for [latex]30[/latex] count

Answer: Brand A costs [latex]$0.12[/latex] per bag. Brand B costs [latex]$0.13[/latex] per bag. Brand A is the better buy.

  Find each unit price and then determine the better buy. Round to the nearest cent if necessary. Brand C Chicken Noodle Soup, [latex]\text{\$1.89}[/latex] for [latex]26[/latex] ounces, or Brand D Chicken Noodle Soup, [latex]\text{\$0.95}[/latex] for [latex]10.75[/latex] ounces

Answer: Brand C costs [latex]$0.07[/latex] per ounce. Brand D costs [latex]$0.09[/latex] per ounce. Brand C is the better buy.